In this section, we describe in detail the
lattice gauge theory of interest,
and the implementation of the numerical algorithms we adopt.
Our software is based upon the HiRep code, originally developed
in the BSM context and presented in Ref. [1]}.
In earlier studies of \(Sp(2N)\)  lattice gauge theories [2]}, [3]},
we both generalised the Cabibbo-Marinari
prescription [4]},
and implemented an efficient resymplectization projection.
For the purpose of this study,
we further wrote original code to implement dynamical
calculations in the presence of
matter in multiple representations.
It is worth reminding the reader that most
lattice code publicly available
has been optimised for QCD and QCD-like theories,
and only a handful of
codes allowing to treat multiple representations exist
(see for instance [5]}, [6]}, [7]}, for \(SU(4)\)  gauge theories).
Hence, we describe our algorithm in some detail, and
we provide a number of tests,
both in this as well as in the
subsequent sections, to demonstrate that our
implementation
reproduces the expected results, in the appropriate limits.
